Corrected temperature sensor measurement

ABSTRACT

Representative implementations of devices and techniques provide correction for temperature sensor measurement error. In an example, the temperature sensor includes an analog-to-digital converter (ADC). The ADC output is error corrected using an iterative digital post-processing technique.

BACKGROUND

The accuracy of integrated temperature sensors and ADCs can potentiallybe limited by semiconductor process parameter variations and/orenvironmental temperature variations. For example, integrated digitaltemperature sensors and ADCs that use a local voltage reference (such asa bandgap-based voltage reference) can be limited by the temperaturevariation of the voltage reference. Bipolar-based reference voltages mayalso be limited by the base-emitter voltage (V_(BE)) variations amongthe devices in a batch. Bandgap-based voltage references can have bothlinear and nonlinear temperature variations due to device physics andmanufacturing tolerances.

To achieve higher accuracy, temperature variations of the voltagereference can be compensated, corrected, or calibrated. In some cases,an analog correction scheme can attempt to provide an accurate voltagereference. Generally, analog correction techniques rely on circuitcompensation and may use analog calibration at one or two knowntemperatures, incurring test time costs. Further, additional voltagereference circuitry may increase complexity and product costs. If ahigher accuracy external voltage reference is used, this may go againstsystem-on-chip integration standards, and may incur additional systemcosts and additional package pins.

Some digital correction techniques can also use calibration at one ortwo known temperatures as well as real time temperature information.Test time costs may be present, depending on the techniques used. Foraccurate post-processing, the temperature needs to be known at the timeof the ADC measurement. This is generally done with an additionaltemperature sensor. Thus, the high accuracy temperature sensor can incurpower and silicon area costs. Further, such sensors typically use an ADCwith a voltage reference, and then the temperature variation of thisvoltage reference needs to be compensated or corrected as well.

In such a case, a classic “chicken and egg” problem is presented. Tomeasure temperature accurately, the voltage reference temperaturevariation needs to be compensated, and that requires the accuratetemperature to be known. For one solution, the voltage reference may beused without digital correction. However, this can degrade the accuracyof the temperature sensor and in turn can degrade the ADC referencecorrection accuracy. For example, in ADC performance, after referencedigital correction using a temperature sensor without referencecorrection, a±0.03% (3σ) gain error inaccuracy can be seen from −40 to+85° C.

BRIEF DESCRIPTION OF THE DRAWINGS

The detailed description is set forth with reference to the accompanyingfigures. In the figures, the left-most digit(s) of a reference numberidentifies the figure in which the reference number first appears. Theuse of the same reference numbers in different figures indicates similaror identical items.

For this discussion, the devices and systems illustrated in the figuresare shown as having a multiplicity of components. Variousimplementations of devices and/or systems, as described herein, mayinclude fewer components and remain within the scope of the disclosure.Alternately, other implementations of devices and/or systems may includeadditional components, or various combinations of the describedcomponents, and remain within the scope of the disclosure.

FIG. 1 is a block diagram of an example ADC/temperature sensorarrangement, wherein the techniques and devices disclosed herein may beapplied.

FIG. 2 is a graphical representation showing potential gain variationsof the ADC of FIG. 1, based on temperature variations of the referencevoltage.

FIG. 3 includes two graphical representations showing potential digitaltemperature sensor gain error and non-linearity error, based ontemperature variations of the reference voltage.

FIG. 4 is a block diagram illustrating an example digital correctionarrangement for temperature variations of the reference voltage,according to an implementation.

FIG. 5 includes two graphical representations showing example solutionvalues based on the example digital correction arrangement of FIG. 4,according to various implementations.

FIGS. 6-9 include graphical representations showing convergence oftemperature sensor error for bandgap non-linearity term and itsapproximation using Taylor polynomial, according to someimplementations.

FIG. 10 is a flow diagram illustrating an example process for correctingtemperature sensor measurement error, according to an implementation.

DETAILED DESCRIPTION Overview

Representative implementations of devices and techniques providecorrection for temperature sensor measurement error. In an example, thetemperature sensor (TS) includes an analog-to-digital converter (ADC).In an implementation, the ADC/TS output is error corrected using aniterative digital post-processing technique, which corrects for voltagereference temperature variation, for example.

In various aspects, two or more iterations of the digitalpost-processing technique are used to converge to the correcttemperature value. In some implementations, the correct temperaturevalue is reached (e.g., convergence) with three iterations or less. Invarious implementations, the iterations provide multiple digitalcorrections, according to a predefined algorithm. In an implementation,a pre-requisite for the iteration algorithm is that the digitalcorrections converge to the correct temperature value.

In one implementation, an initial temperature value is used to startdigital correction of the measured temperature. The initially correctedtemperature value is applied iteratively in subsequent digitalcorrections. In one example, the closer the initial value is to theactual temperature, the better the iteration convergence. In an exampleimplementation, the “raw” output of the temperature sensor (i.e.,without any correction) can be used as the initial temperature value.

In various implementations, digital post-processing is implemented usinghardware and/or firmware. In an implementation, the disclosed iterationalgorithm together with an accurate ADC (Temperature Sensefunctionality), based on digital correction of the voltage reference,offers the following advantages: 1) digital post-processing of thevoltage reference temperature variation leverages digital signalprocessing (DSP) capability, and results in a high accuracy ADC andaccurate temperature measurements; 2) no additional temperature sensoris needed for the technique, saving power and silicon area; 3) a singletemperature measurement is done (e.g., multiple temperature measurementsare not needed to achieve an accurate temperature measurement). In animplementation, this is because digital correction iterations areperformed using digital signal processing, which can be implemented infirmware. The iterative computations are much faster relative totemperature sensor measurement time.

Relative to other solutions that currently use 2 or more ADCs, thedisclosed devices and techniques open up the possibility of using asingle high accuracy ADC for such applications.

Various implementations and techniques for correction of temperaturesensor measurement error are discussed in this disclosure. Techniquesand devices are discussed with reference to example devices and systemsillustrated in the figures that use analog-to-digital converters (ADC),modulators, or like components. However, this is not intended to belimiting, and is for ease of discussion and illustrative convenience.The techniques and devices discussed may be applied to any of variousmodulator or ADC device designs, structures, and the like (e.g.,successive-approximation ADC (SA-ADC), direct-conversion ADC, flash ADC,ramp-compare ADC, integrating ADC (also referred to as dual-slope ormulti-slope ADC), counter-ramp ADC, pipeline ADC, sigma-delta ADC, timeinterleaved ADC, intermediate FM stage ADC, etc.), and remain within thescope of the disclosure.

Implementations are explained in more detail below using a plurality ofexamples. Although various implementations and examples are discussedhere and below, further implementations and examples may be possible bycombining the features and elements of individual implementations andexamples.

Example Temperature Sensor Arrangement

FIG. 1 is a block diagram of an example high resolution digitizer(ADC/TS) arrangement 100, which can be configured as including ananalog-to-digital converter (ADC) or a temperature sensor (TS), whereinthe techniques and devices disclosed herein may be applied. In animplementation, the ADC/TS 100 provides digital information “Dx(T)”representing a measured voltage or temperature. In the implementation,an analog signal representing the voltage or temperature to be measuredis received by the ADC/TS 100 in the form of an analog input voltage“Vin,” or part of V_(REF) (T) (ΔVBE in FIG. 4) which is compared to areference voltage “V_(REF) (T).”

In an implementation, the reference voltage source V_(REF) 104 generatesthe reference voltage V_(REF) (T) based on one or more bandgap voltages(e.g., ΔV_(BE) and V_(BE)) that are derived from a bipolar core withinthe source Vref 104. For example, in an implementation, the referencevoltage V_(REF) (T) is generated based on a base-emitter voltage of oneor more bipolar devices or a difference between base-emitter voltages oftwo or more bipolar devices.

In an implementation, the digital results Dx(T) are generated and outputfrom the ADC portion of the ADC/TS 100. In various examples, the digitalresults Dx(T) are received and interpreted and/or applied byapplications arranged to use the temperature measurement informationDx(T).

For the purposes of this disclosure, a digital result (e.g., digitaloutput) may be described as a digital approximation of an analog input.For example, a digital result may include a digital representation thatis proportional to the magnitude of the voltage or current of the analoginput(s), at a point in time and/or over a selected duration. Thedigital representation may be expressed in various ways (e.g., base 2binary code, binary coded decimal, voltage values, electrical or lightpulse attributes, and the like).

In an implementation, the base-emitter reference voltage V_(BE) and/orthe difference in base-emitter voltages ΔV_(BE) are based on two or morebipolar devices within the bipolar core of the source V_(REF) 104. Thebipolar devices may include bipolar junction transistors, diodes, orlike devices. Alternately, the bipolar devices of the bipolar core maycomprise sub-threshold metal-oxide-semiconductor (MOS) devices,referencing the gate-source voltage (V_(GS)) of the MOS devices as thereference voltage, or like devices. In an alternate implementation, thereference voltage V_(REF) (T) is generated or derived from other devicesor by using other techniques. In alternate implementations, an exampleADC/TS 100 may include fewer, additional, or alternate components,including additional stages of ADCs or different types of ADCs, forexample.

In various implementations, as shown in FIGS. 2 and 3, the voltage ortemperature measurement of a digitizer arrangement (such as ADC/TS 100,for example) may include measurement error due to temperature variationsof the reference voltage V_(REF) (T). For example, as illustrated inFIG. 2, the value of Dx(T) (“Dx”) can increase, for the same inputvoltage Vin (“Vx”), as the temperature of the voltage reference sourceV_(REF) increases (based on the device(s) within the core of the sourceV_(REF) 104). For example, the lines representing T=25° C., T=T₁, andT=T₂ represent temperature variations of the reference voltage V_(REF)(T).

Further, as shown in FIG. 3, the graph at A) shows the case of anuncorrected ADC/TS 100 temperature transfer curve with negative linearand curvature errors. The graph at B) shows the case of an uncorrectedADC/TS 100 temperature transfer curve with positive linear and curvatureerrors. For example, at temperature T=T₁, the uncorrected result (“raw”)is D_(x). In an implementation, D₁ represents an ideal result (such asafter digital correction, for example).

Example Implementations

In various implementations, as shown in FIG. 4, a correction circuit 400may be used with the ADC/TS 100 to correct for the temperaturevariations of the voltage reference V_(REF) (T), and thereby increasethe accuracy of the ADC/TS 100. In an implementation, as illustrated inFIG. 4, the correction circuit 400 is arranged to receive the “raw”output Dx(T) of the ADC/TS 100, digitally process it, and output acorrected digital output value Dy(T). For example, the “raw” outputDx(T) generally includes a measurement value and an error value, asdiscussed above.

In the example ADC/TS 100 illustrated in FIG. 4, the reference voltageV_(REF) (T) is represented by component bandgap voltage values (e.g.,ΔV_(BE) and V_(BE)).

In an implementation, the digital correction performed by the correctioncircuit 400 is based on digital post-processing of the ADC/TS 100results Dx(T), including multiplying Dx(T) by a mathematical functiong(Td) that approximates the inverse of the voltage reference temperaturevariation. In an example, the mathematical function g(Td) can be aTaylor polynomial.

In another implementation, the correction circuit 400 uses an iterativetechnique to correct for the voltage reference temperature variation andto increase the accuracy of the ADC/TS 100 to measure temperature. Forexample, the correction circuit 400 iteratively multiplies the ADC/TS100 digital results Dx(T) by g(Td) until convergence to the corrected(i.e., correct) result Tm. In an implementation, convergence is achievedwhen the error value falls below a predefined threshold value ortolerance (“tol”). For example, in various implementations, themagnitude of the error value is reduced with each iteration (until itconverges).

In an implementation, referring to FIG. 4, the correction circuit 400uses the following iterative technique, described in algorithmic form(with explanation comments):

Tm = Traw # ADC/TS 100 measurement without correction # Td=Traw # chooseinitial temperature to start the iteration # E=1 # initialize the error# FOR E > tol DO # iteration loop #   T = Traw*g(Td) # apply digitalcorrection #   E= T − Td # update error #   Td=T # update correctiontemperature value # END FOR Tm = Td # ADC/TS 100 measurement withcorrection #

In other words, in an implementation, the initial temperature value Tdin the iteration routine may be the “raw” output of the ADC/TS 100,(e.g., Dx(T)), which is the uncorrected temperature measurement (inalternate implementations, another value may be used as the initialtemperature value Td for the iteration routine). The error value “E”represents the difference between consecutive iterations of thecorrected temperature measurement Tm. For a number of iterations, untilthe error value E converges or is less than or equal to the tolerance“tol,” the temperature value Td is multiplied by the mathematicalfunction g(Td) at the correction module 402, and the temperature errorvalue E becomes the value of the result Tm less the current temperaturevalue Td at the digital correction module 402.

The value of the result Tm becomes the new value for Td (e.g., for thenext iteration), and the iterations continue (e.g., via the iterationloop shown in FIG. 4) until E is less than or equal to “tol.” Atconvergence, the output of the ADC/TS 100 Tm is output from the digitalcorrection module 402. This is illustrated in FIG. 4 with the switches Sand S, which close the iteration loop until convergence, and then openthe loop and output the current value for Td (e.g., as the correctedmeasurement value) at convergence which can then be used for V_(REF)correction in ADC measurement of analog input Vin

In an implementation, one module (e.g., the digital correction module402, for example) is arranged to update the error value E with eachiteration while the iteration loop is closed. In the implementation, theupdate includes subtracting the output signal Td from the result Tm ofmultiplying the output signal Td by the correction function g(Td). Inanother implementation, another module (e.g., T module 404, for example)is arranged to update the value of the output signal Td after eachiteration. In the implementation, a value of a “next” output signal isupdated to equal the result T of multiplying a value of a “previous”output signal Td by the correction function g(Td). In variousimplementations, one of the modules (402, 404), or another module orcomponent of the correction circuit 400 is arranged to output thecorrect measurement value (e.g., the most recent value of Td) atconvergence of the error value E.

In various implementations, the modules of the correction circuit 400(e.g., the T module 404 and the digital correction module 402) may beimplemented using digital signal processing components, such asprocessor(s), digital logic, digital filter(s), compression components,and the like. In alternate implementations, fewer, additional, oralternate components or modules may be included in the correctioncircuit 400.

The correction circuit 400 corrects for errors in temperaturemeasurement by the ADC/TS 100, based on temperature variations of thereference voltage V_(REF) (T). In an implementation, a pre-requisite forthe iteration technique is that the digital corrections (e.g., performedby the correction circuit 400) converge to the correct (i.e., actual)temperature value. This is discussed both mathematically and numericallyherein below.

Mathematical Analysis

For temperature T, the ADC/TS 100 output is Dx(T).

Dx(T)=FS*V _(PTAT)(T)/V _(REF)(T),

where FS is the full-scale factor, V_(PTAT) (T) is the lineartemperature input and V_(REF) (T) is the reference voltage.

Define correction function f(T) such that f(T)*V_(REF) (T)=V_(BEO)(Tr),where V_(BEO)(Tr) is a constant value dependent on reference temperatureTr.

Apply digital correction:

Dy(T)=Dx(T)/f(T)=FS*V _(PTAT)(T)/{V _(REF)(T)*f(T)}

Define g(T)=1/f(T)

Dy(T)=FS*V _(PTAT)(T)*g(T)/V _(REF)(T)

V _(REF)(T)=V _(BE)(T)+λ*T=V _(BEO)(Tr)+a*T+c(T)=V _(BEO)(Tr){1+h(T)}

where a is the residual linear term in V_(BE) after Proportional toAbsolute Temperature (PTAT) compensation: a={V_(BE) (Tr)−V_(BE)nom(Tr)}/Tr. V_(BE) nom(Tr) and V_(BE) (Tr) are the nominal and actualsilicon values of V_(BE)(T) at temperature Tr. Due to manufacturingprocess variations, V_(BE) nom(Tr) and V_(BE) (Tr) are generallydifferent, and h(T) includes c(T) the nonlinearity of V_(BE)(T).

The value of a can be measured by single point temperature calibration:

h(T)={a*T+c(T)}/V _(BEO)(Tr)

c(T)=β*(T−Tr−T*Ln(T/Tr))

β=(k/q)*(η−m),

where k is the Boltzmann constant, q is electric charge, and η is thesaturation current temperature exponent.

The value of β depends on physical constants (k,q) as well as processparameters (η, m), which are best obtained by silicon characterization.The value m is the bipolar collector current temperature exponent (for aPTAT design, the value of m is typically less than 1 due to resistortemperature coefficient).

Dy(T)=FS*V _(PTAT)(T)*g(T)/V _(REF)(T)=FS*V _(PTAT)(T)*g(T)/[V_(BEO)(Tr){1+h(T)}]=[FS*V _(PTAT)(T)/V _(BEO)(Tr)]*g(T)/{1+h(T)}.

For an ideal conversion, define:

T=[FS*V _(PTAT)(T)/V _(BEO)(Tr)]

Dy(T)=T*g(T)/{1+h(T)}.

Define temperature error:

Te(T)=Dy(T)−T=T*[g(T)/{1+h(T)}−1]=T*[{g(T)−h(T)−1}/{11+h(T)}].

Define g(T)=1+p(T)

Te(T)=T*{p(T)−h(T))}/{1+h(T)}.

*For an ideal case with known temperature, and perfect correction*

p(T)=h(T) and Te(T)=0.

However, since temperature is not known a priori, an initial value forTd is used:

Te(T)=T*{p(Td)−h(T))}/{1+h(T)}=T*e(T),

where e(T)={p(Td)−h(T))}/{1+h(T)}.

Then, assuming an ideal correction case p(T)=h(T):

e(T)={h(Td)−h(T)}/{1+h(T)}=[a*(Td−T)+c(Td)−c(T)]/[V_(BEO)(Tr)*{1+h(T)}], Dy(T)=T+Te(T)=T+T*e(T)=T*{1+e(T)}.

In an implementation, for some initial value of Dy(T)=Td

Td=T*[1+e(Td)] * actual plus some error term*

Substituting this, with iteration we can write:

e(i+1)=[a*T*e(i)+c(Td)−c(T)]/[V _(BEO)(Tr)*{1+h(T)}],

where e(i) is e(T) at iteration number i.

c(Td)−c(T)=c(T*{1+e(Td)})−c(T)=β*T*[e(Td)*{1−Ln(T/Tr)}−(1+e(Td))*Ln(1+e(Td))].

Using a Taylor series approximation Ln(1+x)≈x−(x²)/2+(x³)/3, anddropping cubic term yields:

c(T*{1+e(Td)})−c(T)≈—β*T*{Ln(T/Tr)+e(Td)/2−e(Td)²/2}*e(Td)=k1*e(Td)+k2*e(Td)²+k3*e(Td)³

where k1=−β*T*Ln(T/Tr), k2=−β*T/2=−k3,

e(i+1)≈[a*T*e(i)+k1*e(i)+k2*e(i)² +k3*e(i)³ ]/[V_(BEO)(Tr)*{1+h(T)}]e(i+1)=b1*e(i)+b2*e(i)² +b3*e(i)³

where b1=(a*T+k1)/[V _(BEO)(Tr)*{1+h(T)}]=T*{a−β*Ln(T/Tr)}/[V_(BEO)(Tr)+aT+c(T)]≈T*{a−β*Ln(T/Tr)}/V _(BEO)(Tr)·b2≈k2/V_(BEO)(Tr)=−βT/{2*V _(BEO)(Tr)}=−b3.

If the magnitude of b1, b2 and b3 are less than 1, then e(i) getssmaller with every iteration and Td converges towards T. For instance,using some example values:

β=(k/q)*(η−m)V/° K=86 μ*(4−1)V/° K=258μV/° K≈0.3m V/° K=0.0003V/° K

a=±40mV/Tr=±40mV/300° K=±0.13m V/° K≈0.2m V/° K

b1@T=600° K≈0.25

b1@T=100° K≈0.05

b2@T=600° K≈0.1

In an implementation, convergence is expected with two or moreiterations. In one implementation, conversion occurs in three or lessiterations. To verify that conversion has occurred to the correct value,the convergence can be verified using the following criterion:

e(T)={h(Td)−h(T)}/{1+h(T)}=[a*(Td−T)+c(Td)−c(T)]/[V_(BEO)(Tr)*{1+h(T)}]→0

which means a*(Td−T)+c(Td)−c(T)→0.

Graphical illustrations in FIG. 5 show two possible solutions, whichindicates that convergence to different values is possible. In FIG.5(A), for the case of T=T₁<Tr and a₁>0 (a<0), apart from a 1^(st)solution T=T₁, there is a 2^(nd) solution T<T₁. For the case of T=T₂>Trand a₂<0 (a>0), apart from a 1^(st) solution T=T₂, there is a 2^(nd)solution T>T₂. In FIG. 5(B), for the case of T=Tr and a₃>0 (a<0), apartfrom the 1^(st) solution T=Tr, there is a 2nd solution T=T₃. For thecase of T=Tr and a₄<0 (a>0), apart from the 1^(st) solution T=Tr, thereis a 2^(nd) solution T=T₄.

In various implementations, there are ways to avoid the occurrence ofmultiple solutions, for instance, by using different initial startvalues to check the final converged values. The mathematical analysisabove was for the ideal case where p(T)=h(T). In alternateimplementations, for the more practical case of p(T) approximating h(T),it can be expected that similar behaviour occurs. In an implementation,the possible multiple solutions still converge to the correct value. Forexample:

Dy(T)=T*g(T)/{1+h(T)}

Iteration=>Dy(Ti+1)=T*g(Ti)/{1+h(T)}

When g(Ti)=1+h(T)=>Dy(Ti+1)=T

thus, convergence for both solutions. In the implementation, it is notnecessary that Ti=T.

Dy(Ti+2)=Dy(Ti+1)=T

The same result is also received for an alternate representation:

Dy(T)=T*{1+e(T)}

e(T)={h(Td)−h(T)}/{1+h(T)}

thus, convergence h(Td)=h(T) for both solutions, and it is not necessarythat Td=T,

=>e(T)=0 and Dy(T)=T.

Thus, the iteration converges.

Numerical Analysis

An example numerical analysis can be shown, using the equations:

Dy(T)=T*g(Td)/{1+h(T)}=T*[1+e(Td)].

For a fixed value of temperature T=T₁

Dy(T ₁)=T ₁ *g(Td)/{1+h(T ₁)}=[T ₁/{1+h(T ₁)}]*g(Td)=Traw*g(Td)=T₁*[1+e(Td)], and

Z(Td)=1+e(Td)=g(Td)/{1+h(T ₁)}={1+p(Td)}/{1+h(T ₁)}

To start, an initial value for Td is selected: Td=initial value near T₁.Then:

-   -   Compute Z(Td)    -   Update Dy(T₁)=T₁*Z(Td)    -   Update Td=Dy(T₁)    -   Iterate Updates.

Example results of the numerical analysis are shown graphically in FIGS.6-9. For example, in the graphs of FIGS. 6-9, the vertical (Y) axisrepresents temperature error=T₁*e(Td), and the horizontal (X) axisrepresents the iteration number. As shown in the graphs, Ta=T₁ is theactual temperature. Various initial values were selected for the initialtemperature Td (labelled as Traw), as shown. A=±40 mV is the residuallinear term in V_(BE) after Proportional to Absolute Temperature (PTAT)compensation [0042]

The graphs of FIGS. 6 and 7 represent the case where p(T)=h(T). Thegraphs of FIGS. 8 and 9 represent the case where p(T)=a 4^(th) orderTaylor polynomial. As shown in FIGS. 6-9, in both cases, convergence isachieved within 3 iterations.

As shown in FIGS. 6-9, the converged error is larger in the exampleTaylor polynomial case, but the fact that the error is the same fordifferent starting values would suggest that it is likely due to thedifference between p(T) and h(T).

e(T)={p(Td)−h(T)}/{1+h(T)}=[p(Td)−{a*T+c(T)}/V _(BEO)(Tr)]/[1+h(T)]→0

Accordingly, the final value is the solution to the equation:

p(Td)−{a*T+c(T)}/V _(BEO)(Tr)=0

In other words, for a certain temperature T₁, the final converged valueof Td is such that:

p(Td)−{a*T ₁ +c(T ₁)}/V _(BEO)(Tr)=0

During the numerical analysis, no convergence to a different significantvalue was observed.

Example Implementations

In various implementations, different mathematical relationships may beused to perform the iterative correction technique by the correctioncircuit 400. Two example algorithms, using different mathematicalrelationships for the iterative digital correction function are shownbelow for illustration. For example, in the second algorithm, thefunction h(T) is approximated by a Taylor polynomial. In otherimplementations, other values and relationships may be used to arrive atthe desired convergence.

Algorithm (1) Tm = Traw # ADC/TS 100 measurement without correction #Td=Traw # choose initial temperature to start the iteration # g(T) = 1 +h(T) # use mathematical function h(T) # h(T) = {a*T + c(T)}/ V_(BEO)(Tr)c(T) = β*(T − Tr − T* Ln(T/Tr)) β = (k/q)*(η − m) E=1 # initialize theerror # FOR E > tol DO # iteration loop #    T = Traw *g(Td) # applydigital correction #    E= T − Td # update error #    Td=T # updatecorrection temperature value # END FOR Tm = Td # corrected temperature #

Algorithm (2) Tm = Traw # ADC/TS 100 measurement without correction #Td=Traw # choose initial temperature to start the iteration # g(T) = 1 +p(T) # p(T) is nth order Taylor polynomial approximation of h(T) # E=1 #initialize the error # FOR E > tol DO # iteration loop #    T = Traw*g(Td) # apply digital correction #    E= T − Td # update error #   Td=T # update correction temperature value # END FOR Tm = Td #corrected temperature #

The techniques, components, and devices described herein with respect tothe example ADC/TS 100 and the correction circuit 400 are not limited tothe illustrations in FIGS. 1-9, and may be applied to other temperaturesensor structures, devices, and designs without departing from the scopeof the disclosure. The correction method can be applied to any measuredparameter X with error h(X) and correction function g(X) in the formD(X)=[X/h(X)]*g(Xd) where D(X) is the measured value and Xd is someinitial estimate of X provided g(Xd) converges to h(X). In some cases,additional or alternative components may be used to implement thetechniques described herein. Further, the components may be arrangedand/or combined in various combinations, while remaining within thescope of the disclosure. It is to be understood that an ADC/TS 100 orcorrection circuit 400 may be implemented as a stand-alone device or aspart of another system (e.g., integrated with other components, systems,etc.).

Representative Process

FIG. 10 is a flow diagram illustrating an example process 1000 forcorrecting temperature sensor measurement error, according to animplementation. The process 1000 describes using a high-resolutiontemperature sensor digitizer (such as the ADC/TS 100, for example) tomake temperature measurements, and a correction circuit (such ascorrection circuit 400) to post-process the digital output of thetemperature sensor to correct the output for error (e.g., due totemperature variation of the reference voltage). The process 1000 isdescribed with reference to FIGS. 1-9.

The order in which the process is described is not intended to beconstrued as a limitation, and any number of the described processblocks can be combined in any order to implement the process, oralternate processes. Additionally, individual blocks may be deleted fromthe process without departing from the spirit and scope of the subjectmatter described herein. Furthermore, the process can be implemented inany suitable materials, or combinations thereof, without departing fromthe scope of the subject matter described herein.

At block 1002, the process includes receiving an output signal from atemperature sensor (such as the ADC/TS 100, for example). In animplementation, the output signal comprises a correct measurement valueand an error value. In an implementation, the process includes digitallypost-processing the output signal from the temperature sensor to correcta temperature measurement represented by the output signal.

In an implementation, the error value is based on a temperaturevariation of a reference voltage of the temperature sensor. For example,in various implementations, the reference voltage is generated based ona base-emitter voltage of one or more bipolar devices or a differencebetween base-emitter voltages of two or more bipolar devices.

At block 1004, the process includes iteratively multiplying the outputsignal by a correction function until convergence of the error valueapproaching zero. In an implementation, the error value converges withinthree iterations, based on the correction function used. For example, inone implementation, the correction function is the mathematical inversefunction of the temperature variation of the reference voltage. Inanother implementation, the correction function comprises a Taylorpolynomial approximation of the inverse function. In an implementation,the process includes iteratively multiplying the output signal by thecorrection function until a magnitude of the error value falls below apredefined threshold value.

In various implementations, the process includes selecting an initialvalue for the temperature value (e.g., the output signal value) to beused with the iterative technique. In one implementation, the processincludes selecting a value of an uncorrected temperature measurementsignal (e.g., “Traw”) of the temperature sensor as the initial value ofthe output signal for a first iteration.

In various implementations, the process includes updating a value of theoutput signal after each iteration. In the implementations, a value of anext output signal is updated to equal the result of multiplying thevalue of a previous output signal by the correction function. Accordingto the process, the “next” output signal then becomes the “previous”output signal for a subsequent iteration.

At block 1006, the process includes outputting the correct measurementvalue. For example, in an implementation, the process includesoutputting the value of the “next” output signal as the correctmeasurement value when the error value converges or is less than orequal to a predefined threshold value.

In alternate implementations, other techniques may be included in theprocess in various combinations, and remain within the scope of thedisclosure.

CONCLUSION

Although the implementations of the disclosure have been described inlanguage specific to structural features and/or methodological acts, itis to be understood that the implementations are not necessarily limitedto the specific features or acts described. Rather, the specificfeatures and acts are disclosed as representative forms of implementingexample devices and techniques.

What is claimed is:
 1. An apparatus, comprising: a first module arrangedto receive an output signal from a temperature sensor, the output signalcomprising a correct measurement value and an error value; and a secondmodule arranged to iteratively multiply the output signal by acorrection function until convergence of the error value.
 2. Theapparatus of claim 1, further comprising an iteration loop between thefirst module and the second module, the iteration loop arranged to beclosed until convergence of the error value.
 3. The apparatus of claim2, wherein the first module is arranged to update the error value witheach iteration while the iteration loop is closed, the update includingsubtracting the output signal from a result of the multiplying theoutput signal by the correction function.
 4. The apparatus of claim 2,wherein the second module is arranged to update a value of the outputsignal after each iteration, wherein a value of a next output signal isupdated to equal a result of multiplying a value of a previous outputsignal by the correction function.
 5. The apparatus of claim 1, whereinone of the first module and the second module is arranged to output thecorrect measurement at convergence of the error value.
 6. The apparatusof claim 1, wherein the correction function comprises an approximationof an inverse of a temperature variation of a reference voltage of thetemperature sensor.
 7. The apparatus of claim 6, wherein the referencevoltage is based on a base-emitter voltage of one or more bipolardevices or a difference between base-emitter voltages of two or morebipolar devices.
 8. The apparatus of claim 1, wherein the second moduleis arranged to iteratively multiply the output signal by the correctionfunction until a magnitude of the error value is less than or equal to apredefined threshold value.
 9. The apparatus of claim 1, wherein amagnitude of the error value is reduced with each iteration.
 10. Asystem, comprising: a temperature sensor; an analog-to-digital converter(ADC) arranged to receive an analog temperature measurement signal fromthe temperature sensor, to compare it to a reference voltage, and tooutput a digital output signal based on the comparison; and a correctioncircuit, comprising: a first module arranged to receive the outputsignal from the ADC, the output signal comprising a correct measurementvalue and an error value based on a temperature variation of thereference voltage; and a second module arranged to iteratively multiplythe output signal by a correction function until convergence of theerror value, the first module or the second module arranged to outputthe correct measurement at convergence of the error value.
 11. Thesystem of claim 10, further comprising a reference voltage sourcearranged to generate the reference voltage based on a base-emittervoltage of one or more bipolar devices or a difference betweenbase-emitter voltages of two or more bipolar devices.
 12. The system ofclaim 11, wherein a value of the base-emitter voltage and a value of thedifference between base-emitter voltages have a temperature variation,and wherein the correction function comprises an approximation of aninverse of the temperature variation.
 13. The system of claim 10,wherein the error value is updated with each iteration based on a resultof the multiplying the output signal by the correction function and amagnitude of the error value decreases with each iteration untilconverging.
 14. A method, comprising: receiving an output signal from atemperature sensor, the output signal comprising a correct measurementvalue and an error value; iteratively multiplying the output signal by acorrection function until convergence of the error value; outputting thecorrect measurement value.
 15. The method of claim 14, furthercomprising digitally post-processing the output signal from thetemperature sensor to correct a temperature measurement represented bythe output signal.
 16. The method of claim 14, further comprisingiteratively multiplying the output signal by the correction functionuntil a magnitude of the error value falls below a predefined thresholdvalue.
 17. The method of claim 14, further comprising selecting a valueof an uncorrected temperature measurement signal of the temperaturesensor as an initial value of the output signal for a first iteration.18. The method of claim 14, further comprising updating a value of theoutput signal after each iteration, wherein a value of a next outputsignal is updated to equal a result of multiplying a value of a previousoutput signal by the correction function.
 19. The method of claim 18,further comprising outputting the value of the next output signal as thecorrect measurement value when the error value converges or is less thanor equal to a predefined threshold value.
 20. The method of claim 14,wherein the error value is based on a temperature variation of areference voltage of the temperature sensor.
 21. The method of claim 20,wherein the correction function approximates an inverse of thetemperature variation of the reference voltage.
 22. The method of claim14, wherein the correction function comprises a Taylor polynomial or anymathematical function approximation.
 23. The method of claim 14, whereinthe error value converges within a finite number of iterations, based onthe correction function.
 24. A system comprising: a high-resolutiontemperature sensor (TS); an analog-to-digital converter (ADC) arrangedto receive an analog temperature measurement signal from the TS, and tooutput a digital output signal based on the analog temperaturemeasurement signal and a bandgap-based reference voltage; and acorrection circuit including digital signal processing components andarranged to perform multiple digital corrections on the digital outputsignal based on an iterative algorithm, the correction circuitcomprising: a first module arranged to receive the output signal fromthe ADC, the output signal comprising a correct measurement value and anerror value based on a temperature variation of the bandgap-basedreference voltage; and a second module arranged to iteratively multiplythe output signal by a correction function comprising an approximationof an inverse of a temperature variation of the bandgap-based referencevoltage, until convergence of the error value, the first module or thesecond module arranged to output a corrected temperature measurementvalue when the error value converges.